We present the concept of the topological symmetry group as a way to analyze the symmetries of non-rigid molecules. Then we characterize all of the groups which can occur as the topological symmetry group of an embedding of the complete graph K_{4r+3} in S^3.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,878 papers · 148 categories
Trend · papers per month
48 results for “non-rigid molecules”
New method reconstructs moving parts of proteins in cryo-EM.
problem Reconstructing non-rigid molecules with moving parts in cryo-EM.
method Graph Laplacian construction from multiple projection images, followed by spectral volume expansion.
result High-resolution visualization of molecular dynamics using spectral volumes.
Non-rigidity of hyperbolic manifold under scalar curvature constraints.
problem Non-rigidity of hyperbolic manifold under scalar curvature constraints.
method Compactly supported deformations, topological constraints.
result Non-rigidity under scalar curvature constraints, rigidity under topological constraints.
A new method for non-rigid point set registration reduces computational complexity.
problem Efficiently registering non-rigid point sets with large numbers of points.
method Structured Analytic Coherent Point Drift (Analytic-CPD) reformulates CPD for structured analytic mappings.
result Analytic-CPD reduces computational complexity by controlling the deformation model's dimensionality.
New benchmark for non-rigid 3D human shape retrieval.
problem Distinguishing between body shapes of 3D human models.
method Extended benchmark with 145 new models and FAUST dataset.
result Improved comparison of 25 shape retrieval methods.
The study proves rigidity and non-rigidity of spherical caps in mean curvature.
problem Understanding mean curvature rigidity and non-rigidity on spherical caps.
method Used a Tangency Principle to prove rigidity and constructed counterexamples for non-rigidity.
result Contrast between rigidity and non-rigidity phenomena on spherical caps.
Projective structures are mostly rigid at the boundary but some are not.
problem Boundary rigidity of projective structures.
method Investigation of projective structures on manifolds with boundary.
result Existence of non-rigid projective structures and characterization of them.
In this paper we study a novel class of parabolic geometries which we call parabolic geometries of Monge type. These parabolic geometries are defined by special gradings of simple Lie algebras, namely, gradings with the property that their -1 component contains a nonzero co-dimension 1 abelian subspace whose bracket wi…
New non-rigid discrete groups found in hyperbolic spaces.
problem Uniqueness of conformal or spherical CR structures on spheres.
method Nilpotent Sierpiński carpet and stretching to construct non-rigid groups.
result Discrete hyperbolic groups can have non-rigid deformations.
The Novikov Conjecturemath.GT
We give a survey on recent development of the Novikov conjecture and its applications to topological rigidity and non-rigidity. .
Non-rigidity degree of a lattice , nrd, is dimension of the L-type domain to which belongs. We complete here the table of nrd's of all root lattices and their duals; namely, the hardest remaining case of , and the case of are decided. We describe explicitly the -type domain …
We give a counterexample of Bowers-Stephenson's conjecture in the spherical case: spherical inversive distance circle packings are not determined by their inversive distances.
Paper proposes a method to design molecules with specific properties.
problem Designing molecules with desired chemical and biological properties.
method Energy-based model in latent space, SGDS algorithm for gradual distribution shifting.
result Method achieves strong performances on various molecule design tasks.
Deep generative models are able to suggest new organic molecules by generating strings, trees, and graphs representing their structure. While such models allow one to generate molecules with desirable properties, they give no guarantees that the molecules can actually be synthesized in practice. We propose a new molecu…
Although machine learning has been successfully used to propose novel molecules that satisfy desired properties, it is still challenging to explore a large chemical space efficiently. In this paper, we present a conditional molecular design method that facilitates generating new molecules with desired properties. The p…
A new model designs molecules with desired properties.
problem Finding molecules with optimal chemical or biological properties.
method A latent prompt Transformer model with three components: latent vector, molecule generation, and property prediction.
result The model achieves state-of-the-art performance on molecule design tasks.
In de novo drug design, computational strategies are used to generate novel molecules with good affinity to the desired biological target. In this work, we show that recurrent neural networks can be trained as generative models for molecular structures, similar to statistical language models in natural language process…
SILVR generates new molecules fitting protein binding sites.
problem Generating novel small molecule compounds for drug design.
method Selective Iterative Latent Variable Refinement (SILVR) for diffusion-based molecule generation.
result SILVR can generate new molecules similar in shape to original fragments without protein knowledge.
GCDM generates valid large 3D molecules and optimizes existing molecules.
problem Lack of geometric properties in 3D molecule generation models.
method Introduces Geometry-Complete Diffusion Model (GCDM) using equivariant GNNs.
result Significantly outperforms existing models in 3D molecule generation and optimization.
Modof-pipe optimizes molecules by modifying a single site, outperforming state-of-the-art methods.
problem Improving drug candidates' properties through chemical modification.
method Deep generative model Modof over molecular graphs for molecule optimization.
result Modof-pipe achieves significant improvements in octanol-water partition coefficient and molecule similarity constraints.
FREED++: Improving RL Agents for Fragment-Based Molecule Generation by Thorough Reproductionq-bio.BM
Improved RL model for fragment-based molecule generation.
problem Generating molecules with high docking scores.
method Thorough reproduction, scrutiny, and improvement of the FREED model.
result The improved model produces molecules with superior docking scores.
CORE optimizes molecules by copying or generating substructures, improving accuracy.
problem Inaccurate substructure prediction in molecule optimization.
method Copy & Refine (CORE) strategy combining scaffolding tree generation and adversarial training.
result Significant improvement in various molecule optimization metrics.
A new method improves molecule generation accuracy and efficiency.
problem Posterior collapse in VAEs for molecule sequence generation.
method Re-balancing reconstruction loss to avoid posterior collapse.
result Our method achieves state-of-the-art reconstruction accuracy and competitive validity.
We tackle here the problem of multimodal image non-rigid registration, which is of prime importance in remote sensing and medical imaging. The difficulties encountered by classical registration approaches include feature design and slow optimization by gradient descent. By analyzing these methods, we note the significa…
Generative model learns to create molecules with multiple properties using interpretable substructures.
problem Creating molecules with multiple chemical properties is challenging.
method Compose molecules from substructures identified as responsible for each property, using graph generative models.
result Significant improvements in accuracy, diversity, and novelty of generated compounds over state-of-the-art baselines.
A new deep model generates molecules by fragments, improving validity and uniqueness.
problem Generating valid and unique molecules using deep learning.
method Develops a language model for molecular fragments, using frequency-based masking.
result Significantly outperforms other language model-based competitors in molecule generation.
We present a framework, which we call Molecule Deep -Networks (MolDQN), for molecule optimization by combining domain knowledge of chemistry and state-of-the-art reinforcement learning techniques (double -learning and randomized value functions). We directly define modifications on molecules, thereby ensuring 100…
New method learns shape correspondences robustly from raw geometry.
problem Inaccurate and poor generalization of shape correspondences.
method Learning-based approach with feature-extraction network and functional map representation.
result Robust and accurate shape correspondence learning with less training data.
In this paper, we discuss the Weyl problem in warped product space. We obtain the openness, non rigidity and some applications. These results together with the a priori estimates obtained by Lu imply some existence results. Meanwhile we reprove the infinitesimal rigidity in the space forms.
Predicting Drug Interactions and Mutagenicity with Ensemble Classifiers on Subgraphs of Moleculesstat.ML
In this study, we intend to solve a mutual information problem in interacting molecules of any type, such as proteins, nucleic acids, and small molecules. Using machine learning techniques, we accurately predict pairwise interactions, which can be of medical and biological importance. Graphs are are useful in this prob…
Explicit solutions to the Riemann-Hilbert problem will be found realising some irreducible non-rigid local systems. The relation to isomonodromy and the sixth Painleve equation will be described. Keywords: Riemann-Hilbert problem, Painleve equations, algebraic solutions, Heun equations, tetrahedral/octahedral group, tr…
Generative neural network designs novel 3D molecules with specified properties.
problem Designing molecules with desired properties in chemistry.
method Conditional generative neural network for 3D molecular structures.
result Demonstrated utility in generating novel molecules with specified motifs or composition.
Equivariant diffusion model generates 3D molecules efficiently.
problem Generating high-quality 3D molecules efficiently.
method Equivariant Diffusion Model (EDM) that operates on atom coordinates and types.
result Significantly outperforms previous methods in molecule quality and training efficiency.
Searching new molecules in areas like drug discovery often starts from the core structures of candidate molecules to optimize the properties of interest. The way as such has called for a strategy of designing molecules retaining a particular scaffold as a substructure. On this account, our present work proposes a scaff…
A new method matches similar regions in non-rigid shapes using spectra of differential operators.
problem Evaluating similarity of non-rigid shapes with partiality.
method Alignment of spectra of differential operators (SI-LBO and regular LBO) on a manifold with multiple metrics.
result Matching spectra outperforms competing methods on standard benchmarks.
Recent methods for generating novel molecules use graph representations of molecules and employ various forms of graph convolutional neural networks for inference. However, training requires solving an expensive graph isomorphism problem, which previous approaches do not address or solve only approximately. In this wor…
Bayesian optimization improves molecule design by addressing three pitfalls.
problem Bayesian optimization pitfalls cause poor performance in molecule design.
method Identified and addressed three pitfalls: incorrect prior width, over-smoothing, and inadequate acquisition function maximization.
result Basic BO setup achieves highest performance on PMO benchmark.
The discovery of novel materials and functional molecules can help to solve some of society's most urgent challenges, ranging from efficient energy harvesting and storage to uncovering novel pharmaceutical drug candidates. Traditionally matter engineering -- generally denoted as inverse design -- was based massively on…
Designing a new drug is a lengthy and expensive process. As the space of potential molecules is very large (10^23-10^60), a common technique during drug discovery is to start from a molecule which already has some of the desired properties. An interdisciplinary team of scientists generates hypothesis about the required…
New model generates larger molecules more effectively.
problem Previous graph generation techniques struggle with larger molecules.
method Hierarchical graph encoder-decoder using structural motifs.
result Model significantly outperforms previous baselines on molecule generation tasks.
Site-specific graph neural network for predicting protonation energy of oxygenate moleculesphysics.chem-ph
Graph neural network predicts protonation energies of oxygen atoms in bio-oil molecules.
problem Predicting protonation energies of oxygen atoms in bio-oil molecules for chemical upgrading.
method Site-specific graph neural network approach using iterative local nonlinear embedding.
result Effective prediction of protonation energies of individual oxygen atoms in bio-oil molecules.
AI and HPC help screen millions of molecules for SARS-CoV-2 treatments.
problem Finding effective treatments for SARS-CoV-2.
method AI and HPC enable screening of large molecule datasets.
result Data release of 23 datasets with 4.2 billion molecules.
Paper introduces a graph-based approach for retrosynthesis prediction.
problem Predicting precursor molecules for target molecules in organic synthesis.
method Graph-based approach that predicts graph edits and synthons expansion.
result Achieves top-1 accuracy of 53.7%.
A new graph model HMG and neural network HMGNN improve molecule property predictions.
problem Predicting quantum mechanical properties of molecules with limited consideration of many-body interactions.
method Introducing heterogeneous molecular graphs (HMG) and building HMGNN on neural message passing scheme.
result HMGNN achieves state-of-the-art performance in 9 out of 12 tasks on the QM9 dataset.
Molecular optimization aims to discover novel molecules with desirable properties. Two fundamental challenges are: (i) it is not trivial to generate valid molecules in a controllable way due to hard chemical constraints such as the valency conditions, and (ii) it is often costly to evaluate a property of a novel molecu…
CogMol designs novel drug-like molecules for SARS-CoV-2 targets.
problem Designing efficient drugs for novel viral proteins.
method End-to-end framework combining VAE, controlled sampling, and predictors.
result Highly selective and affinity molecules for SARS-CoV-2 targets.
A set of molecular descriptors whose length is independent of molecular size is developed for machine learning models that target thermodynamic and electronic properties of molecules. These features are evaluated by monitoring performance of kernel ridge regression models on well-studied data sets of small organic mole…
VecMol generates 3D molecules as continuous vector fields, overcoming modality and geometry constraints.
problem Challenges in generating 3D molecules, especially in drug discovery and materials science.
method VecMol reimagines molecular representation by modeling 3D molecules as continuous vector fields over Euclidean space, parameterized by a neural field and generated using a latent diffusion model.
result Vector-field-based representations show promise for 3D molecular generation, validated on benchmarks.